What is the solution for (dy)/(dx)=18xsec(y) ?

The solution for (dy)/(dx)=18xsec(y) is y=arcsin(9x^2+c_{1})+2pin,y=pi+arcsin(-9x^2-c_{1})+2pin

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(dy)/(dx)=18xsec(y)

\frac{d y}{d x} = 18 x sec (y)

y = arcsin (9 x^{2} + c_{1}) + 2 πn, y = π + arcsin (- 9 x^{2} - c_{1}) + 2 πn

Solution steps

\frac{d y}{d x} = 18 x sec (y)

Solve separable ODE:

y = arcsin (9 x^{2} + c_{1}) + 2 πn, y = π + arcsin (- 9 x^{2} - c_{1}) + 2 πn

y = arcsin (9 x^{2} + c_{1}) + 2 πn, y = π + arcsin (- 9 x^{2} - c_{1}) + 2 πn

\frac{d y}{d t} = \frac{t ^{2} y + y}{t + 1}

d x = \frac{x}{1 - x} d t

(1 - y) y^{^{'}} = x^{2}

(p - 1) y^{^{'}} (p) + 3 y (p) = 0

y^{^{'}} - y - 1 = 0

What is the solution for (dy)/(dx)=18xsec(y) ?
The solution for (dy)/(dx)=18xsec(y) is y=arcsin(9x^2+c_{1})+2pin,y=pi+arcsin(-9x^2-c_{1})+2pin